7 people can paint 5 walls in 42 minutes. How many minutes will it take for 10 people to paint 9 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 5\text{ walls}\\ p &= 7\text{ people}\\ t &= 42\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{5}{42 \cdot 7} = \dfrac{5}{294}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 10 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{5}{294} \cdot 10} = \dfrac{9}{\dfrac{25}{147}} = \dfrac{1323}{25}\text{ minutes}$ $= 52 \dfrac{23}{25}\text{ minutes}$ Round to the nearest minute: $t = 53\text{ minutes}$